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Two 2-connected (n, n +4) determination of the chromatic

Then for any edge of G e, has [Received Date] 2008-11 A O4 [Author] Yang Jinmei (1981 a), F, Qinghai music are people, Master, mainly in graph theory, the first 64 of the total T Dali University Natural Science G) = P (G-e) A G. e) (: l =) where G-e is removed from the edge e G be the graph, G. e G the edge e is removed and the two end points coincide, and the event of heavy side, leaving only one side of the graph obtained. Through the transformation () is also equivalent to G) = G + e) + G. e), where G + e is an edge added to G e. Lemma 2. Empty graph Q and the complete graph of the chromatic polynomials are P (Q, A) = A, P (K, A) = A (A-1) ... (A One Where +1) Lemma 3 [. If G is a G. And G, _ bond graph, then == P (K) A (A a 1) ... (A-r +1) x Lemma 4. If G is a non-trivial block containing r said, said, ... a connected graph, then G, A) = Ⅱ Jp (Day, A) / A. Lemma 5. Let graph G has two blocks. And, if I () {≥ 3 (= 1,2), then the graph G is the color is not unique. The paper used is shown in Figure 1. Take it F'DEFH ◇ roar E7E8E9E (7) F8F9 (≥ 8) 1 2 The main results Lemma and its proof sketch of Theorem 1. Figure E and F are not the only color. Proof: According to Lemma 5, Figure E is clearly not the only color. By Lemma 3 have P (E):, obtained by the Lemma 2,4 AP (F): blue -|:}:( A a 1 ))(:( A A 1) P (). 'Mapping E and the point of bonding by Figure F, is clearly P (,):( A-1) Dan: P (F), but the F palm, so the map F is not the only color. Theorem 2. Figure E is not just a color a graph. Proof: According to Lemma 1. canthal $ 2,3 Figure 2 has a bearing section 64 ◇ 2 Cut two 2 Jan boxes connected (n, +4) around the fist set 8g color Gui Volume 8 Take a [ORDER +] alum canthal an iv = a P (E.) = P () = one examination a ◆ one.: a) A: a) A clear Jp () = P (), but the degree of sequence E is (2,2,3,3,3,3,3,3,4), the degree sequence is (2,3,3,3,3,3,3,3,3), thus. Palm,[link widoczny dla zalogowanych], so the only E and not the color. Theorem 5 ~, (≥ 8) is not chromatically unique. Proof: some point to and label as follows: 3 Total 64 Dali College of Natural Sciences are corpse according to Lemma 1,4 (E) = P () = l22 hail n. 5n. 6n. 6n a 7 a ● ---- ● i ■ ∈ _ --- ● i a n. 6n. 7: _P (A_P (A clear Jp ()), but the degree sequence is (2,2, ... 2,3,3,3,3,3,3,4), the degree sequence is (2,2, ... 2,3,3,3,3,3,3,3,3), from the - and E to get, so, and not the color only. [
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